![]() Other methods are iterative in time, where state integration is learned with a variational approach, step-by-step Li and Benjamin ( 2017) Endo et al. Extensions of the Variational Quantum Eigensolver have been developed where low-energy subspaces are identified, then integrated in time by scaling their eigenenergies Heya et al. Variational methods for dynamical simulation break down into conceptually distinct approaches. ( 2019) provide a promising alternative approach. ![]() Noisy, Intermediate-Scale Quantum (NISQ) devices, Variational Quantum Algorithms Peruzzo et al. ( 2015), and qubitization methods Low and Chuang ( 2019), may lead to prohibitively deep circuits for current quantum computers. I Introductionĭynamical simulation algorithms designed for the fault-tolerant era, such as Trotterization methods Lloyd ( 1996) Sornborger and Stewart ( 1999), LCU methods Berry et al. Our numerical simulations verify that VHD can be used for fast-forwarding dynamics. Our proof relies on locality of the Hamiltonian, and hence we connect locality to trainability. Moreover, we prove that the VHD cost function does not exhibit a shallow-depth barren plateau, i.e., its gradient does not vanish exponentially. We prove an operational meaning for the VHD cost function in terms of the average simulation fidelity. It also removes Trotterization error and allows simulation of the entire Hilbert space. VHD allows for fast forwarding, i.e., simulation beyond the coherence time of the quantum computer with a fixed-depth quantum circuit. We propose a new algorithm called Variational Hamiltonian Diagonalization (VHD), which approximately transforms a given Hamiltonian into a diagonal form that can be easily exponentiated. In this work, we aim to make variational dynamical simulation even more practical and near-term. ![]() This has led to recent proposals for variational approaches to dynamical simulation. However, the circuit depth of standard Trotterization methods can rapidly exceed the coherence time of noisy quantum computers. Dynamical quantum simulation may be one of the first applications to see quantum advantage. ![]()
0 Comments
Leave a Reply. |